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Radiation pressure and the Stefan-Boltzmann law

In a previous post on Kirchhoff's law (1859) and black bodies , we saw that the energy density of thermal radiation is a function of temperature only. The first measurements of thermal radiation (from hot platinum wire) were made by Tyndall, and from his results Stefan concluded, in 1879, that the energy radiated went as the fourth power of the absolute temperature. This empirical relationship was later theoretically determined, for black bodies, by Boltzmann in 1884. The law that bears both their names is:

\[ R_B = \sigma T^4 \]

and \(\sigma\) is known as the Stefan-Boltzmann constant, and \(R_B\) is the emissive power, the radiant power emitted per unit area.

Thermal radiation, Kirchhoff's law, and black bodies

All matter continuously emits electromagnetic radiation as a consequence of its temperature. This radiation is called thermal radiation or heat radiation (although of course it isn't intrinsically different from electromagnetic radiation generated by any other means). Thermal radiation is what makes thermal imaging possible, and why hot embers glow, etc. From our everyday experience and from experimentation we can see that both the wavelength and intensity of radiation emitted depend in some way on the temperature of the matter.